Strasburg (2-5) had not won since an opening day decision over Miami. He struck out four, walked three and the only run he allowed came on a ground out.
Rafael Soriano relieved Strasburg in a non-save situation and worked around a one-out single in the ninth.
Adam LaRoche got the Washington offense started with a two-run homer in the fourth. Stephen Lombardozzi singled in a run in the fifth and came around to score later in the inning along with Denard Span on a base hit by Ryan Zimmerman.
Bryce Harper tacked on a run with a homer in the seventh, his 11th of the season.
Edinson Volquez (3-4) took the loss, giving up five runs on five hits in five innings while striking out seven.